Built to comply with the championship's new Group C regulations which were introduced in 1982, the car was a replacement for Porsche's successful 936 model which competed in the previous Group 6 category of the World Championship. The project began in June 1981, and the first prototype chassis was completed on March 27, 1982, in time for the beginning of the World Championship season. Jürgen Barth tested the first chassis at Porsche's private test track.

The 956 features a chassis made of an aluminium monocoque, a first for the company, helping to allow the car to meet the 800 kg (1,764 lb) weight minimum in Group C. The engine is the same as the one used in the Porsche 936/81, the Type-935 2.65 L turbocharged Flat-6, producing approximately 635 hp (474 kW) (originally developed as an Indycar engine; hence the cubic capacity used). The very first dual clutch gearbox was also designed for the 956, mated to a traditional 5-speed manual.

An improved chassis with better fuel efficiency from a BoschMotronic electric system was developed for 1984, being termed the 956B. In total, twenty-eight 956s would be built by Porsche from 1982 to 1984, with an unofficial 29th chassis built from spare parts by Richard Lloyd Racing. The 956 was also the first Porsche to have ground effect aerodynamics.

In 1983, 956 chassis #107 was used by Porsche as a testbed for their P01 Formula One engine, later badged as TAG and used exclusively by McLaren. The car was able to test some of the characteristics of a Formula One car in order to develop the engine. The engine became highly successful in F1, and while never the most powerful on the grid, between 1984 and 1987, the turbocharged TAG-Porsche would win 25 Grands Prix and help McLaren to two Constructors and three World Driver's Championships. As of the 2012 German Grand Prix, the TAG-Porsche engine sits in 7th place on the list of F1 race winning engines.

The 956 would be officially replaced by the Porsche 962 in 1985, an evolution in the 956's design.

The 956 made its debut at the Silverstone 6 Hour race, the second round of the World Championship for Makes with Jacky Ickx and Derek Bell driving for the factory. After missing the following round at the 1000 km Nürburgring for developmental reasons, the Ickx/Bell unit reappeared at the 24 Hours of Le Mans. They led the race for the entire 24 hours, eventually taking the overall win - their third win together. As they had already won in 1981 with a Porsche 936 that had used an early version of the 956 engine, their car had start number 1. The two other factory 956 followed them, so the three factory Porsches finished 1-2-3 in the order of their starting numbers.

The overall all-time lap record for the demanding 20 km Nürburgring-Nordschleife circuit in the Eifel Mountains was achieved during the qualifying session for the 1983 1000km of Nürburgring, by Stefan Bellof, who drove his 956 around in 6 minutes 11.13 seconds, at an average speed of 202 km/h (126 mph). The race lap record is held by the same Bellof, during the 1983 1000 km Nürburgring, the lap being clocked at 6:25.91.

At the 1985 1000 km of Spa, Bellof died after colliding with Jacky Ickx's newer 962. Safety concerns over the 956 led to its eventual end as teams upgraded to the safer 962. The 956's last win would come courtesy of Joest Racing in the last race of the 1986 WEC season, in what also turned out to be the 956's last race.